Optimized RF shield design

ABSTRACT

Radio frequency (RF) shields used with magnetic resonance imaging (MRI) apparatus may experience gradient field induced eddy currents and RF field induced eddy currents. These eddy currents can cause the RF shield to heat up at an undesirable rate. RF shields are designed to have a desired degree of RF shielding and a desired heating attribute. Design goals for RF shields include gradient field transparency and RF field opacity, both of which can be influenced by eddy currents. Example methods identify a gradient field that will induce eddy currents and identify an RF field that will induce eddy currents. If a region on the RF shield is identified where the desired heating attribute will not be achieved, then a pattern of axial cuts and azimuthal cuts can be made in the RF shield to reduce gradient eddy current heating in the RF shield while maintaining desired RF shielding.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 13/407,852, filed Feb. 29, 2012.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialthat is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction of the patent document or thepatent disclosure as it appears in the Patent and Trademark Officepatent file or records, but otherwise reserves all copyright rightswhatsoever.

BACKGROUND

Magnetic resonance imaging (MRI) apparatus typically employ threegradient coils to produce spatially selective information encoding in asample. The three gradient coils contain numerous turns of conductivewires and produce gradients that may be pulsed on and off. MRI apparatusalso use radio frequency (RF) transmit coils to produce spin excitationin a sample. An RF shield may be placed between a set of RF transmitcoils and the gradient coils to prevent the RF field produced by the RFtransmit coils from interacting with the gradient coils.

An ideal RF shield would be completely transparent to the gradient fieldproduced by the gradient coils and completely opaque to the RF fieldproduced by the RF transmit coils. Being completely opaque (e.g.,completely blocking the RF field from interacting with the gradientcoils) is a design goal because an interaction between the RF coils andthe gradient coils could produce an RF energy loss that would appear asa lowering of the quality factor Q of the RF coil and would decrease thesignal-to-noise ratio (SNR) of signal received from the sample.

Two types of eddy currents may be produced in an RF shield interposedbetween gradient coils and RF transmit coils. The gradient coils mayinduce eddy currents in the RF shield and the RF transmission coils mayalso induce eddy currents in the RF shield. The eddy currents havedifferent properties. RF shields are designed to disrupt the gradientcoil induced eddy currents and to not disrupt the RF transmission coilinduced eddy currents.

Conventional RF shields are made of a copper-dielectric-copper laminatestructure with slits in both copper layers. The slits on the copperlayers of the RF shield are designed to suppress gradient eddy currentheating while still allowing the RF shield to reduce coupling betweenthe RF and gradient systems. The slits need to be placed to reducegradient eddy currents while still allowing a return path for RF eddycurrents. Therefore, capacitors may be positioned to span a slit in thecopper so that RF eddy currents have a return path and are notdisrupted. The capacitors form a high-pass filter that allows the RFeddy currents to flow and thus shield the RF coil field. The capacitorsalso impede gradient eddy currents that might negatively impact thegradient field. Unfortunately, having too many slits and too manycapacitors may produce undesirable results. The undesirable results maybe produced in traditional RF shields that have hundreds of capacitorsplaced around multiple small cross-cuts with both axial and azimuthaldirections.

The undesirable results include, for example, capacitors being impactedby ohmic heating. Ohmic heating may affect capacitor lifetimes,capacitor failure rates, and melting of soldered bases. As temperaturesincrease in hybrid systems using split coils, ohmic heating issues withcapacitors may also increase. Therefore reducing the numbers of slitsand thus the number of capacitors may produce improved results.Additionally, cutting slits in the copper sheets introduces holesthrough which RF energy can pass. Having RF energy pass through the RFshield makes the RF shield less opaque to the RF field and allowsconditions where there could be an interaction between the RF system andthe gradient system.

One conventional RF shield includes slits that follow RF currentstreamlines on the RF shield. While this conventional shield may beappropriate for some applications, it may not be appropriate forcircular or “quadrature” excitation where the RF current streamlinerotates with the Larmor frequency over the RF shield. As the currentstreamline rotates with the Larmor frequency it may pass over slits thatare fixed in space and thereby allow RF leakage.

Eddy currents that are induced in an RF shield due to the pulsinggradient field can reduce penetration of the gradient field into theimaging volume and may give rise to ohmic heating in the RF shield. Thisheating in the RF shield may be more pronounced for some rapid imagingtechniques (e.g. echo planar imaging (EPI)) and for hybrid MRI systemsconfigured with split gradient coil designs.

MRI-guided hybrid systems are becoming more important due to advantagesthey provide over traditional MRI systems. In some MRI-guided hybridsystems, the MRI scanner is split into two halves in order toaccommodate complementary diagnostic and therapeutic equipment forperforming radiotherapy, positron emission tomography (PET), surgery(e.g., ablation), and other applications. In addition to the gap in theMRI main magnet, the X, Y and Z gradient coils may be split.

Gradient coil patterns for hybrid systems may be bunched more closelynear gaps in the split coils. FIGS. 1 and 2 illustrate the bunching ofgradient coil wires near the gap forming the split between portions ofthe gradient coil. The closer bunching of gradient coil patterns mayexacerbate heating because of stronger local magnetic fields near thedenser collection of gradient coil wires. FIG. 1 illustrates a splittransverse gradient coil 100. Coil 100 is separated from RF transmitcoils 110 by an RF shield 120. Note the different density of coil wiresin regions 112 and 114 of coil 110. FIG. 2 illustrates a splitlongitudinal gradient coil 200. Coil 200 is separated from RF transmitcoils 210 by an RF shield 220. Note the different density of coil wiresin regions 212 and 214 of coil 210. The higher density of coil wires inregions 114 (FIG. 1) and 214 (FIG. 2) produce stronger local fields thatcan increase ohmic heating in specific regions on an RF shield. Theohmic heating is produced by oscillating eddy currents produced by rapidpulses in the gradient coils. The concentration of coil wires in regions114 (FIG. 1) and 214 (FIG. 2) may concentrate ohmic heating. Thus, theissue of ohmic heating may be exacerbated on RF shields used in splitgeometries as compared to non-split geometries.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate various example systems, methods,and other example embodiments of various aspects of the invention. Itwill be appreciated that the illustrated element boundaries (e.g.,boxes, groups of boxes, or other shapes) in the figures represent oneexample of the boundaries. One of ordinary skill in the art willappreciate that in some examples one element may be designed as multipleelements or that multiple elements may be designed as one element. Insome examples, an element shown as an internal component of anotherelement may be implemented as an external component and vice versa.Furthermore, elements may not be drawn to scale.

FIG. 1 is a schematic perspective view of a split transverse gradientcoil separated from an RF birdcage body coil by an RF shield.

FIG. 2 is a schematic perspective view of a split longitudinal gradientcoil separated from an RF birdcage body coil by an RF shield.

FIG. 3 is a section view illustrating field lines corresponding to amain magnet field B₀, an RF field B₁ produced by a body coil, and aY-gradient field B_(G).

FIG. 4 illustrates a simulation result for eddy current density over atraditional RF shield with a plurality of axial slits and no azimuthalslits.

FIG. 5 illustrates a rectangular portion of an RF shield having a longedge a and a short edge b.

FIG. 6 is a planar (rolled-out) view of an RF shield that includes bothazimuthal slits and axial slits.

FIG. 7 illustrates four slit patterns in a copper strip.

FIG. 8 illustrates experimental results tracking temperature increasesin a copper strip.

FIG. 9 illustrates a correlation between eddy current distribution andtemperature distribution.

FIG. 10 illustrates a simulation result for eddy current density over anRF shield with greater length in the Z direction.

FIG. 11 illustrates a planar (rolled-out) view of an RF shield thatincludes both azimuthal slits and axial slits.

FIG. 12 illustrates a longer RF shield.

FIG. 13 illustrates RF induced current density distributions on an RFshield.

FIG. 14 illustrates an azimuthal integration of current density.

FIG. 15 illustrates RF shields with azimuthal slits in two differentpositions relative to cold bands.

FIG. 16 illustrates a method associated with designing an RF shield.

FIG. 17 illustrates a portion of a method associated with designing anRF shield.

FIG. 18 illustrates an apparatus configured to design an RF shield.

FIG. 19 illustrates an apparatus configured to design an RF shield.

FIG. 20 illustrates an RF shield.

DETAILED DESCRIPTION

Example apparatus and methods design and/or produce a radio frequency(RF) shield for use in magnetic resonance imaging (MRI) systems. In oneembodiment, an RF shield may be a portion of a hollow cylinderfabricated with one or more sheets of shaped and slotted copperconnected by a dielectric material. In one example, the shield may befashioned on a printed circuit board and thus slits may be cut all theway across a copper sheet. The RF shield is configured to be positionedbetween a set of gradient coils in an MRI system and a set of RFtransmit coils. Slots may be cut on the copper on each surface of theshield to disrupt gradient eddy currents induced on the RF shield andthereby reduce ohmic heating. Capacitors may be added as bridges overthe slots to mitigate issues associated with disrupting thehigh-frequency RF eddy currents induced on the RF shield. Cutting slotsand using thin sheets of copper facilitates suppressing gradient eddycurrent heating. While conventional axial slot patterns have providedsome heating suppression, hybrid MRI systems may require an improveddesign of both axial and azimuthal slots to achieve adequate heatingattributes in for RF shields in hybrid MRI systems.

Therefore, in one embodiment, example apparatus and methods optimizeslit patterns for RF shields for use in hybrid MRI systems. In oneexample, optimal slit patterns maximize gradient penetration through theRF shield and minimize RF penetration through the RF shield whilemaintaining desired temperature performance on the RF shield. Gradienteddy currents are effectively reduced by restricting the lengths of theaxial slits in a central region of the RF shield and then by placing asmall number of azimuthal slits centered on “cold” bands outside of thecentral region of the RF shield.

FIGS. 1 and 2 illustrate how an RF shield may be positioned between agradient coil and an RF body coil. The RF shield and RF body coil mayboth be positioned within the bore of an MRI system. RF shields havebeen used to separate gradient coils and RF coils for years. However,new types of MRI apparatus (e.g., split systems) and new types of MRIoperations (e.g., quadrature) have been introduced.

Thus, in one embodiment, example apparatus and methods produce an RFshield that suppresses gradient induced eddy current heating using aminimal number of slits on the RF shield. Reducing the number of slitsmay also facilitate reducing the number of capacitors. In oneembodiment, placement of the slits is based, at least in part, onnumerical simulations. While a general combination of axial andazimuthal incisions on an RF shield to suppress the gradient eddycurrent heating has been described, the axial pattern was consideredcollectively with the azimuthal pattern rather than performing separateanalysis and design for the axial slits and the azimuthal slits. Thus,example apparatus and methods may perform a multi-part iterativeanalysis that considers axial slits and azimuthal slits separately toprovide improved heat suppression. Fingerprint-like incision patternscalculated to follow RF eddy current flow have provided some suppressionin linearly polarized RF transmission but have not been applicable toquadrature operation. Thus, example apparatus and methods may size andposition slots based, at least in part, on quadrature operationconsiderations.

FIG. 3 illustrates a field B0 produced by the main magnet in an MRIsystem. This field B0 is produced along the Z-axis. The homogeneity ofthe field is on the level of several parts per million (ppm) in theregion of interest. Three sets of gradient coils (Gx, Gy, Gz) providelinearly spatially dependent Z-components of their fields. Gradient coil300 is illustrated producing a gradient field that is normal to thesurface of RF shield 310 in the “gap” region 320 where the gradient coil300 is split. Gradient coils like split gradient coil 300 may producegradients using pulses that produce pulsating magnetic flux. Pulsatingmagnetic flux may induce an electric current that circulates around theRF shield 310 in the general pattern of an image current. Pulsatingmagnetic flux may lead to ohmic heating of the RF shield 310, and, insome cases, that heating may reach an undesirable or unacceptable level.Conventional shields addressed ohmic heating by introducing axial slitsinto an RF shield. However, shields to be used in hybrid MRI systems mayrequire an improved design.

FIG. 4 illustrates an RF shield 400 that includes a conventional patternof axial slits 430. FIG. 4 illustrates gradient coil 410 as twomirror-image gradient fingerprints. The gradient coil 410 and RF shield400 are illustrated as an unrolled planar sheet.

Current flowing through the gradient coil 410 will induce eddy currentson RF shield 400. The relative strengths of the eddy currents areillustrated through gray scale shading where stronger eddy currents arelighter and weaker eddy currents are darker. In one example, eddycurrent densities for the RF shield 400 may be computed by solving theelectromagnetic Maxwell equations associated with the gradient currentsand the planar sheet. Solving the Maxwell equations may reveal a “cold”(e.g., dark) region 420 where there is minimal eddy current ohmic power.Solving the Maxwell equations may also reveal a “hot” (e.g., white)region 450 where there is maximal eddy current ohmic power. The higheddy current ohmic power may be localized in the end ring region 460 ofa conventional RF shield 400. Example apparatus and methods facilitateadding 360-degree azimuthal slits to the end ring region 460 to producean improved RF shield with more effectively suppressed eddy currentheating. In one embodiment, the position(s) of the azimuthal slit(s) inthe end ring region 460 can be determined based, at least in part, on anelectromagnetic analysis that details the effectiveness of an azimuthalcut pattern in suppressing ohmic heating.

FIG. 5 illustrates a planar rectangular copper strip 500 with dimensionsa and b (a>b). The copper strip 500 may be subjected to a field with acomponent normal to the strip 500. The dashed line 510 represents theposition of a slit at y=y₀ parallel to the x-axis. Theoretical analysisand experimental results reveal that the area on a copper strip in an RFshield that receives the largest normal flux will experience thegreatest ohmic heating.

An estimate of the electric field induced on the copper due to thepulsing gradient can be computed using Faraday's law in electrodynamics.If E is the magnitude of the average circulating electric field aroundthe edge of the copper strip, ω is the angular frequency (frequency ofoscillation) and B is the peak magnitude of the normal magnetic field,then the voltage drop around the edge is related to the magnetic fluxthrough the strip by:

$E \cong \frac{\omega\;{Bab}}{2\left( {a + b} \right)}$

For the case where a>>b, then E would be dominantly determined by itsproportionality to the short edge according to:

$E \cong {\frac{1}{2}\omega\;{Bb}}$

If a single cut is made parallel to the short edge (b) across the centerof the strip, and if a/2 is still much larger than b, E will remainapproximately dominated by the short-edge factor b. Thus the ohmic powerdensity σE², for electrical conductivity σ, is also dominated by b. If,on the other hand, a cut is made parallel to the long edge (a), andagain across the center of the strip, the factor b, and the electricfield, are halved as described by:

$E \cong {\frac{1}{2}\omega\; B\frac{b}{2}}$

Halving the electric field creates a condition where the eddy currentpower loss becomes approximately one fourth of that in a similar copperstrip that has no cuts or that has a single center cut parallel to theshort edge.

Example apparatus and methods may therefore determine where to placeaxial and azimuthal slits based, at least in part, on understandingpower losses for various conducting two-dimensional shapes. For arectangular shape with sides a and b, an estimate for the total,time-averaged, power loss due to a uniformly normal magnetic field B₀oscillating at frequency ω is found to be:

$\begin{matrix}{\left\langle P \right\rangle \approx {0.035\omega^{2}\beta_{0}^{2}\sigma\; d\frac{a^{3}b^{3}}{a^{2} + b^{2}}}} & \lbrack 1\rbrack\end{matrix}$

According to Equation [1], the average power volume density over thestrip is approximately proportional to:

$\begin{matrix}{P \propto \frac{a^{2}b^{2}}{a^{2} + b^{2}}} & \lbrack 2\rbrack\end{matrix}$

If a>>b, the long edge a will be cancelled out in both the denominatorand numerator, and the average power will be approximately proportionalto, and dominated by, the short edge b. Placing an azimuthal cut halvesthe short edge. Halving the short edge reduces the average power densityto ¼ of what it was without the azimuthal slit.

For a spatially non-uniform field, it may be more involved to determinewhere to place a cut. As a special case for a non-uniform field,consider a magnetic field with a linear y-gradient in its z-component,B_(z)(x,y)=B₀+G·y, impressed upon a copper strip. A cut parallel to thelong edge of the strip will divide the strip into two parts. If the eddycurrent power loss for each part is represented by <P₁> and <P₂>, and if<P> represents the power loss without any cuts, the curves pertaining tothe power loss ratio (<P₁>+<P₂>)/<P> for different cut positions(different slit positions y₀) are shown in FIG. 9. As will be shownlater, optimal cut positions correspond to the locations where the powercurves reach their minima.

FIG. 6 illustrates a flattened view of one half of an X-gradient coil610 for a split MRI system. X gradient coil 610 is positioned over anexample cylindrical RF shield 600. The X-gradient coil 610 and the RFshield 600 are shown unwrapped and with axial slits 630 and azimuthalslits 650. The dashed lines identify the dominant heating regions 620produced by gradient eddy currents. A Y-gradient coil pattern andheating area may be found by shifting the X-gradient coil 610 pattern byan amount corresponding to 90 azimuthal degrees. Example apparatus andmethods may identify the dominant heating regions 620 and place theazimuthal slits 650 based, at least in part on the identification of thedominant heating regions 620.

FIG. 7 illustrates one pattern of axial and azimuthal cuts in a copperstrip. Four classes of incisions (a), (b), (c), and (d) were made on thestrip 700. Temperature was measured at the position indicated by theblack dot 710. Strip length a=400 mm and width b=80 mm are indicated.

Experimental results reveal heat suppression produced by azimuthal cutsin example RF shields produced by example methods and apparatusdescribed herein. In one experiment, a rectangular copper strip similarto strip 700 with dimensions 400 mm×80 mm×0.03 mm was placed under agradient coil. The copper strip was positioned under the fingerprint eyeof a split gradient coil so that an azimuthal cut in the copper stripwould bisect the copper strip along its long axis. Gradient currentflowing in the gradient coil was pulsed at 1500 Hz. Experiments wereperformed with 1 axial cut, 3 axial cuts, 7 axial cuts, and 1 azimuthalcut as illustrated in FIG. 7. An optical thermometer was used to monitorthe temperature evolution as a function of time. In one experiment,temperature was monitored at a single mid-point on the copper strip. Inanother experiment, current was allowed to flow and temperatureincreases were measured over time.

Example results are illustrated in FIG. 8. FIG. 8 illustratestemperature curves for four cut patterns. FIG. 8 illustrates that, asexpected, a single axial cut across the copper strip resulted in only aminor decrease in the peak temperature. FIG. 8 also illustrates that, asexpected, a single azimuthal cut reduced the temperature peak by afactor of approximately ¼ (7.5 K relative to 32 K). This measured resultagrees well with the analytical result that the electric field should behalf, the power loss should be 25% relative to a strip with no cuts, andthat the temperature peak should also be 25% of the temperature peak ofthe strip with cuts. This correlation between analytical results andobserved results informs two different embodiments of a method foridentifying cut patterns. In one embodiment, cut patterns can bedetermined analytically. In another embodiment, cut patterns can bedetermined by actually making cuts and observing results. In eitherembodiment, cuts can be designed or fabricated iteratively until adesired temperature attribute is achieved while maintaining desired RFshielding properties.

Table 1 compares temperature measurements, 2D analytical results, and 3Dnumerical simulations for the temperature curves illustrated in FIG. 8.

TABLE 1 Peak Measured 2D power 3D power Numbers Temperature ratiosratios simula- and kinds increases normalized calculated by tions for ofcuts (measured) to zero cuts Eq. [2] the ratios 0 32.7 K 1 1 1 1 cutparallel 31.4 K 0.96 0.90 0.95 to the short dimension 3 cuts parallel17.9 K 0.55 0.63 0.56 to the short dimension 7 cuts parallel  7.2 K 0.220.29 0.235 to the short dimension 1 cuts parallel  7.8 K 0.24 0.26 0.26to the long dimension

Example apparatus and methods may use formulae that describe eddycurrent power loss to determine where to position slots that will reduceohmic heating. In one embodiment, slot position can be determined basedon eddy current simulations due to the theoretical and observedcorrelation between eddy current power loss and temperature. FIG. 9illustrates a correlation between temperature distribution 1210 on an RFshield and eddy current distribution 1200 on the RF shield. In general,a heat equation may be employed to connect the eddy current heating tothe temperature of the copper strip for purposes of identifying slotlocations. For an experimental copper strip, the temperature T obeys athermal diffusion equation:

$\begin{matrix}{{\rho\; c\frac{\partial{T\left( {x,y} \right)}}{\partial t}} = {{k\;{\nabla^{2}{T\left( {x,y} \right)}}} + {{J^{2}\left( {x,y} \right)}/\sigma} - {{{hT}\left( {x,y} \right)}/d}}} & \lbrack 3\rbrack\end{matrix}$

Here, T is the shield temperature relative to a fixed ambienttemperature. p, c, k, σ, J and h are the mass density, specific heat,thermal conductivity, electrical conductivity, eddy current density(A/m²) and total heat transfer (surface) coefficient, respectively.Equation [3] illustrates that the temperature time-rate of change isdetermined by a combination of spatial-diffusion, eddy current heating,and cooling terms. Equation [3] can be solved by 2D finite elementmethods. However, in one embodiment, example apparatus and methods maynot consider the spatial diffusion term and may focus on therelationship between temperature and ohmic power. In this case Equation[3] will become a first-order differential equation, and the solutionfor a given position x, y, is found to be:

$\begin{matrix}{T = {\frac{J^{2}d}{\sigma\; h}\left( {1 - {\exp\left( {- \frac{ht}{c\; d\;\rho}} \right)}} \right)}} & \lbrack 4\rbrack\end{matrix}$

Equations [2, 4] provide the relation between the temperature and thedimensions of the strip by:T∝J ² ∝P∝a ²+b²)  [5]

The proportionality relation between the temperature and the eddycurrent power loss in equation [5] implies that making cuts to reducepower loss will directly carry over to temperature suppression. Sinceequation [4] shows proportionality to the thickness d of the strip, inone embodiment, example apparatus and methods use thin material for anRF shield.

Based on the analytical and experimental results, example methods andapparatus may configure axial slits to suppress gradient induced eddycurrents in a central region of an RF shield and may also configureazimuthal slits to suppress gradient induced currents in an outer regionof an RF shield. The axial slits and the azimuthal slits are configuredto not disrupt RF induced eddy currents. Since the RF induced eddycurrents in the RF shield by the RF transmit coil flow axially in thecenter region of the RF shield, the axial slits will not block the RFcurrent. Leaving the RF current unblocked facilitates maintaining RFshielding while allowing the gradient field produced by the gradientcoil to penetrate the RF shield and reach the imaging volume.Suppressing gradient induced eddy currents suppresses heating.

One approach for identifying slit locations involves analyzing asimulation result of power ratio versus the slit position y₀ (unit: b)for a copper strip. FIG. 10 illustrates the results of one experimentwhere a copper strip with an aspect ratio a/b=5 was placed under amagnetic field with different strength of gradient g=G·b/2B₀. Circles onthe curves indicate where the electric field vanishes when no cuts arepresent. The locations where the electric field vanishes are called a“cold” region. Example apparatus and methods may place azimuthal cutsbased on the locations of the cold regions.

In FIG. 10, curve 900 corresponds to the homogeneous case (g=0) wherethe optimal cut position is found at the center where the power loss hasbeen reduced to 25% of the original loss. For inhomogeneous fields(curves 910, 920, 930, 940), the optimal cut position deviates from thecenter of the curve. However the “cold” regions where the electric fieldvanishes are fairly close to the optimal cut positions identified by theminimum for each of curves 910, 920, 930, and 940. Thus, in oneembodiment, example apparatus and methods achieve eddy current powersuppression and thus ohmic heating suppression by identifying “cold”bands where the electric field is close to a minimum. Numericalsimulations can be employed to find the “cold” lines for the narrowstrip region. Example apparatus and methods may then position azimuthalslits along these “cold” lines.

Turning now to FIG. 11, in one analysis, an eddy current ohmic loss inRF shield 1000 was normalized to 1.000 in arbitrary units. RF shield1000 includes central axial cuts 1040. RF shield 1000 was subjected to afield produced by split gradient coil 1050. The pair of azimuthal slits1010 suppressed the heating of RF shield 1000 down to 0.211 arbitraryunits. This represents a 79% reduction in heating.

In one experiment, after the pair of azimuthal slits 1010 were produced,the RF shield 1000 was further analyzed. The analysis revealed that twoheating bands remained. Therefore two more pairs of azimuthal slits 1020were placed parallel to the two “cold” centers of the bands. Addingthese additional azimuthal slits 1020 to the RF shield 1000 producedadditional suppression. Experimental results showed that ohmic powerloss was reduced to 0.0424. This represents a 96% eddy currentsuppression, which corresponded to a 96% heating reduction. Thereforeexample apparatus and methods may employ an iterative approach wherecuts are placed and heating analysis, either theoretical or observed, isrepeated until a termination condition is met.

Different RF shields will have different shapes and sizes. Additionally,different MRI systems will have gradient coils with different sizes andshapes. Hybrid MRI systems may have split gradient coils. Thus hybridMRI systems may have a gap in both the main magnet and the gradientcoils. Different hybrid systems may have different gaps between theportions of the main magnet or gradient coils. Therefore example methodscan be configured to determine the position of a minimum eddy currentregion and then to position the axial cuts and azimuthal cuts based, atleast in part, on the location of the minimum eddy current region. Theposition of a minimum eddy current region may depend on the size of theRF shield and the relative position of the RF shield and gradient coilwires.

Unlike conventional systems, example apparatus and methods may seek toimprove or even optimize both axial and azimuthal slots. A traditionalRF shield has a plurality of axial cuts in its central region. Exampleapparatus and methods may find a common length of these axial slots. Byway of illustration, a birdcage coil can be approximated by an RFconducting cylinder that assumes the current density is continuouslydistributed instead of flowing along discrete rungs. Using thisassumption, the induced RF eddy current density on a “long” shield canbe found in terms of a stream function according to:

$\begin{matrix}{{{{J_{\phi}\left( {\phi,z} \right)} = {\frac{\partial}{\partial z}{S\left( {\phi,z} \right)}}};}{{J_{z}\left( {\phi,z} \right)} = {{- \frac{1}{R_{s}}}\frac{\partial}{\partial\phi}{S\left( {\phi,z} \right)}}}} & \lbrack 6\rbrack\end{matrix}$

where the stream function for a long continuous cylindrical shield isgiven by:

$\begin{matrix}{{{S\left( {\phi,z} \right)} = {\int_{0}^{\infty}{{A(k)}\frac{R_{c}I_{1}^{\prime}\left( {kR}_{c} \right)}{R_{s}{I_{1}^{\prime}\left( {kR}_{s} \right)}}\sin\;{{\phi cos}({kz})}d\; k}}}{with}} & \lbrack 7\rbrack \\{{A(k)} = \frac{2{I\left( {{\cos\left( {kZ}_{1} \right)} - {\cos\left( {kZ}_{2} \right)}} \right)}}{\pi\;{k^{2}\left( {Z_{2} - Z_{1}} \right)}}} & \lbrack 8\rbrack\end{matrix}$

Here, I is the maximum current in an end ring chosen to be an azimuthalstrip similar to an actual birdcage coil where the axial currents areassumed to be returned. While a birdcage coil is described, exampleapparatus and methods may be configured to determine slots for RFshields that will be placed between gradient coils and other types of RFtransmit coils. I₁ is the first order modified Bessel function. Z₁ andZ₂ are defined to be the positive lengths from the axial center of coilsat z=0 to the center of the end ring strip. R_(c) and R_(s) are therespective radii of the cylinder approximating the birdcage and the RFshield. In quadrature operation, the currents corresponding to Equations[6] and [7] rotate with Larmor frequency around the z-axis. In oneembodiment that seeks to optimize slot placement, example apparatus andmethods seek the domain [+Z_(c), +Z_(c)] where the axial component RFinduced current density is dominant:∫₀ ^(π) |J _(z)(ϕ,z)|dϕ>∫ ₀ ^(π) |J _(ϕ)(ϕ,z)|dϕ for z∈[−Z _(c) ,+Z_(c)]  [9]

Example apparatus and methods then restrict axial slots to lie withinthe axial component dominant region defined by the inequality inEquation [9]. This step is configured to minimize the width of theend-ring azimuthal strip without impeding the azimuthal RF inducedcurrent return on the shield.

Example apparatus and methods may find a pattern of axial cuts to beused as the starting point for the azimuthal cut determination. Thismulti-step approach may be employed to achieve minimum ohmic heating forthe combined set of azimuthal and axial cuts. Recall that axial cutscannot extend so far that RF eddy currents on the shield induced by theRF transmit coil have no return path.

Example apparatus and methods may use Equations [6]-[8] to compute theRF eddy currents induced by an RF transmit coil onto a solid coppershield with no cuts. Shields of different length may be analyzed. In onesimulation, the parameters of Equations [7, 8] were set to R_(c)=30 cm,R_(s)=32 cm, Z₁=25 cm, Z₂=26 cm, and the maximum current in the end ringwas normalized to unity.

The magnitude distributions for both azimuthal and axial components ofthe RF eddy currents are shown in FIG. 13. The ϕ component illustratedon the left side (a) is mainly restricted to the end regions, while theZ component illustrated on the right side (b) is dominant over the broadmiddle region on the shield surface. Example apparatus and methods mayconsider these results for an RF transmit coil in quadrature mode, whereboth J_(ϕ) and J_(z) are rotating around the z-axis at the Larmorfrequency. Example apparatus and methods may design slit patterns withazimuthal symmetry.

FIG. 13 illustrates RF induced current density distributions on a longRF shield as computed via Equations [7, 8] with given parameters. Notethat the gray scales for the ϕ component (a) and Z component (b) of theRF eddy current density are different to illustrate their variations asa function of azimuthal angle ϕ and axial distance z. To prevent thedisruption of the azimuthal RF eddy currents, the extent to which theaxial slots are limited in the z direction is indicated by the whitedashed lines in the figure.

To determine which component (ϕ, Z) is dominant at a particular zposition, integration along the azimuthal direction is carried out asshown in FIG. 14. FIG. 14 illustrates normalized current componentsafter integration over the total azimuthal angle. The circledintersections 1410 and 1420 are the points that divide the shield into aZ-component-dominant region and ϕ-component-dominant region. For thisexample, z∈(−20 cm, 20 cm) is the Z-component-dominant region.

In one embodiment, example apparatus and methods seek to lengthen theaxial slits as much as possible without impeding the RF eddy currentreturn paths. For a given RF transmit coil and RF shield, exampleapparatus and methods determine the RF current Z component dominantregion as shown through the simulations of the RF shield eddy currentdensity. The axial slit length is then restricted accordingly. Thisoptimal choice is then input to processing configured to place theazimuthal cuts to further reduce gradient current heating.

Returning briefly to FIG. 4, in one embodiment, after the axial cutshave been optimized, the azimuthal cuts may be optimized. A 3D simulatededdy current pattern in the end region of an unwrapped finite-lengthshield with only axial slits is shown in FIG. 4. The use of a planar(e.g., unwrapped) geometry provides a good approximation by comparingsimulations with and without the strip curvature. This is understandablebecause the cylindrical RF shield is in close proximity to thecylindrically curved gradient coils. FIG. 4 illustrates an eddy currentmagnitude distribution from a simulation of the unwrapped RF shieldgiven an optimized pattern of axial slits. The current magnitudes followthe scheme indicated by the vertical gray scale bar in arbitrary units.A pair of squeezed fingerprint coils 410 with a gap between them ismodeled to mimic the behavior of a transverse gradient coil in a splitMRI system. Two horizontal azimuthal “cold” bands 420 where minimizedheating would occur are evident near the “eyes” of the gradient wirepatterns 410.

Cuts made along the big dimension and centered on “cold” bands where theelectric field vanishes are an effective way to suppress eddy currentheating. Thus, for a single pair of fingerprints characterizing a singletransverse gradient coil, gradient simulations confirm that oneazimuthal cut going through the “cold” band 420 and completelycircumscribing the shield 400 (e.g., subtending 360 degrees) is a goodchoice for an end region. To compare the relative effectiveness ofdifferent RF shield designs for heat reduction, analyses were conductedthat normalized the total eddy-current ohmic power deposited on an RFshield with no azimuthal cuts as illustrated in FIG. 4. A pair ofazimuthal slits made in the cold bands as illustrated in FIG. 6 lead toa 79% reduction in heating (from 1.00 to 0.21). The cold bands bisectthe strip regions for the dimensions of this model, but this will notgenerally be true for longer shields where the normal component of thegradient field may be less homogeneous.

FIG. 12 illustrates a longer RF shield 1100. RF shield 1100 isillustrated interacting with gradient coil 1110. FIG. 12 illustrates theminimum eddy current region 1107 farther out in the axial direction ofRF shield 1100 when compared to shorter RF shields.

Since different RF shields may interact with different gradient coils indifferent MRI apparatus, one example method may include identifying thecentral bands of minimum eddy current. In one embodiment, the centralbands of minimum eddy current may be identified using numericalsimulations. The example method may then position azimuthal cuts based,at least in part, on the location of the central bands of minimum eddycurrent as determined by numerical simulation.

Minimum eddy current regions depend on the size of the RF shield and therelative position of the gradient coil wires. However, as illustrated inFIG. 12, larger shield lengths do not move the location of the minimumeddy current significantly farther out in the axial direction. Instead,the location of the minimum eddy current remains closely connected tothe gradient fingerprint pattern. Therefore example apparatus andmethods may place slots based on the gradient fingerprint pattern.

If two transverse gradient coils are symmetrically constructed (e.g.,offset from each other by 90 degrees), then pairs of azimuthal cuts canaddress heating problems for both sets of gradient coils. Exampleapparatus and methods may add azimuthal cuts until a desired heatingattribute is achieved. For example, additional cuts can be placed overthe new cold bands identified after placing the first azimuthal cut. Indifferent embodiments, a total of three azimuthal cuts in a given endregion may be employed or two azimuthal cuts could be placed to trisecta strip. Example apparatus methods may consider the homogeneity of thegradient field when deciding whether to place one, two, three, or moreazimuthal cuts. In general, example apparatus and methods may achieveazimuthal slit optimization for a given gradient coil by using numericalsimulations to find the minimum ohmic power loss, and then placingazimuthally circumscribed cuts accordingly. The optimized slits patternmay be found iteratively until the temperature level is decreased to adesirable range.

FIG. 15 compares the difference between azimuthal slits made through thecold bands 1520 and away from those bands at a location 1530. The leftside of FIG. 15 illustrates the effect of an azimuthal slit 1510 madethrough the center of the cold bands 1520. The right side of FIG. 15illustrates the effect of an azimuthal slit 1540 made at a location 1530other than through the center of the cold bands. The power reduction forslit 1510 is about 80%, and the maximum value of eddy current density is0.26 arbitrary units compared with 1.05. On the right side, a pair 1540of cuts 2 cm away from the center of the cold bands produced anapproximate 50% power reduction and an eddy current density peak valueis 0.41.

One example method begins by using a high-frequency 3D electromagneticsolution logic for the RF eddy current patterns to establish the limitson the axial-cut lengths. With a first iteration of a single azimuthalcut that approximately bisects the end strips, a 3D electromagneticsolution logic for low-frequency gradient eddy currents (typicallyfinite-element) can be used to find the degree to which the ohmic powerhas been reduced. If more reduction is needed, and if the “cold band” isnot at the center, the single azimuthal cut can be moved to align withit in the simulation. If more azimuthal cuts are needed, they can beequally spaced in first approximation, and the 3D EM solution logic usedagain to find the heating reduction. If more reduction is sought, theazimuthal-cut spacing can be adjusted so that the multiple cold bandsfound are at the midpoints of the new positions.

Example apparatus and methods may place optimized slots on both sides oftwo layered RF shields. The two layers may each have their owncapacitance bridges. The different layers may be off-set (e.g., rotatedslightly) from each other to avoid having single incisions penetrate thewhole RF shield. The rotation mitigates RF field leakage.

Example apparatus and methods may use two or more thin copper stripsinstead of one thick copper strip because there is a proportionalityrelation between temperature increase and the thickness of the strip.Thinner copper lowers the temperature. However, a minimum thicknessneeds to be maintained for effective shielding.

One example method may iterate to find new minimum eddy current regionsand to identify a location(s) for another slit(s) until a desiredtemperature suppression has been achieved. In another example theiteration may continue until a threshold number of slits has beenidentified. Recall that a minimal number of slits may be desired toreduce the possibility of RF leakage through the RF shield to thegradient coil.

In one embodiment, electromagnetic simulations are performed where thegradient-induced eddy current distributions on the RF shield are foundby solving Maxwell equations. In different simulations the gradientfield frequency may be modeled at different frequencies. In oneembodiment, the gradient field frequency is set at 1500 Hz to resemble afrequency that corresponds to EPI-like sequences.

Both analytical and observed techniques may concentrate on eddy currentsdue to just the X or Y gradient coils. These transverse gradient coilsgenerate large normal magnetic field components relative to the RFshield surface. The large normal magnetic field components are the mainsource of eddy current heating. Example methods and apparatus may ignoreheating due to the Z gradient coil.

Having described the general theory upon which some example apparatusand methods may be based, this section provides greater mathematicaldetail for one example analytical calculation of eddy currents for arectangular strip immersed in a normal inhomogeneous field oscillatingwith a frequency ω. This analysis facilitates understanding howdifferent example apparatus and methods may determine where to placeslots to minimize or reduce total ohmic power deposited on a strip. Theorigin of the coordinate is chosen at the center of strip. The method ofseparation of variables is used to solve the corresponding partialdifferential equations (12, 13). Faraday's and Ohm's laws provide twoequations, respectively, for the electric and magnetic fields andcurrent density,

$\begin{matrix}{{\nabla{\times \overset{->}{E}}} = {- \frac{\partial\overset{->}{B}}{\partial t}}} & {A.\lbrack 1\rbrack} \\{\overset{->}{J} = {\sigma\;\overset{->}{E}}} & {A.\lbrack 2\rbrack}\end{matrix}$

with σ the strip conductivity. For thin strips, ignore the currentdensity in the normal direction (the z axis) and combine A. [1], A. [2]to give

$\begin{matrix}{\left( {\frac{\partial J_{y}}{\partial x} - \frac{\partial J_{x}}{\partial y}} \right) = {{- j}\;{\sigma\omega}\; B_{z}}} & {A.\lbrack 3\rbrack}\end{matrix}$

By continuity of the current density ∇·{right arrow over (J)}=0, astream function U can be introduced and defined as:

$\begin{matrix}{{{J_{x}{\hat{e}}_{x}} + {J_{y}{\hat{e}}_{y}}} = {\frac{1}{d}{\nabla{\times \left\lbrack {{U\left( {x,y} \right)}{\hat{e}}_{z}} \right\rbrack}}}} & {A.\lbrack 4\rbrack}\end{matrix}$

where d is the thickness of the strip and in terms of x and y unitvectors. Thus, the current density of x and y components can bedetermined from the stream function as follows:

$\begin{matrix}{{J_{x} = {\frac{1}{d}\frac{\partial{U\left( {x,y} \right)}}{\partial y}}},{J_{y} = {{- \frac{1}{d}}\frac{\partial{U\left( {x,y} \right)}}{\partial x}}}} & {A.\lbrack 5\rbrack}\end{matrix}$

Substituting A.[5] into A.[3], produces a Poisson equation for thestream function (14)∇² U(x,y)=jσdωB _(z)(x,y)  A.[6]

By assuming current flows parallel to the edge at the boundary, thestream function satisfies the Dirichlet boundary Γ condition given byU(x,y)|_(Γ)0  A.[7]

For an arbitrary magnetic field profile, the stream function can beexpanded in a series of harmonics,B _(z)(x,y)=ΣC _(e,e) x ^(e) y ^(e) +ΣC _(o,e) x ^(o) y ^(e) +ΣC _(e,o)x ³ y ^(o) +ΣC _(o,o) x ^(o)  A.[8]

Here, C's are coefficients with subscripts e and o denoting even and oddorder, respectively. In order to satisfy the boundary condition A.[7],the harmonic combinations for integers n, m and strip boundariescorresponding to the length a and width b are

$\begin{matrix}{{x^{e}y^{e}\text{:}\mspace{14mu}\cos\frac{\left( {{2n} - 1} \right)\pi\; x}{a}\cos\frac{\left( {{2m} - 1} \right)\pi\; y}{b}}{x^{o}y^{e}\text{:}\mspace{14mu}\sin\;\frac{2n\;\pi\; x}{a}\cos\frac{\left( {{2m} - 1} \right)\pi\; y}{b}}{x^{e}y^{o}\text{:}\mspace{14mu}\cos\frac{\left( {{2n} - 1} \right)\pi\; x}{a}\sin\;\frac{2m\;\pi\; y}{b}}{x^{o}y^{o}\text{:}\mspace{14mu}\sin\frac{2n\;\pi\; x}{a}\sin\frac{2m\;\pi\; y}{b}}} & {A.\lbrack 9\rbrack}\end{matrix}$

For the strip subjected to a static field plus a y-gradient field,B _(z)(x,y)=B ₀ +G·y  A.[10]the Poisson equation can be separated into two parts∇² U=∇ ² U ₁+∇² U ₂ jωdσB ₀ +jωdσG·y  A.[11]

In A.[11], U₁ corresponds to the homogeneous part B₀ and U₂ correspondsto the y-gradient part G·y. Both can be expanded by the correspondingharmonic terms shown previously in A.[9]:

$\begin{matrix}{{U_{1}\left( {x,y} \right)} = {\sum\limits_{n,{m = 1}}^{\infty}{A_{n,m}\cos\; v_{n}x\;\cos\;\mu_{m}y}}} & {A.\lbrack 12\rbrack} \\{{U_{2}\left( {x,y} \right)} = {\sum\limits_{n,{m = 1}}^{\infty}{C_{n,m}\cos\; p_{n}x\;\sin\; q_{m}y}}} & {A.\lbrack 13\rbrack} \\{{{v_{n} = \frac{\left( {{2n} - 1} \right)\pi}{a}},{\mu_{m} = \frac{\left( {{2m} - 1} \right)\pi}{b}}}{p_{n} = {{\frac{\left( {{2n} - 1} \right)\pi}{a}\mspace{14mu} q_{m}} = {\frac{2m\;\pi}{b}\mspace{14mu}\left( {n,{m = 1},2,{3\mspace{14mu}\ldots}}\mspace{14mu} \right)}}}} & {A.\lbrack 14\rbrack}\end{matrix}$

With Fourier expansions of B₀ and G·y:

$\begin{matrix}{B_{0} = {\sum\limits_{n,{m = 1}}^{\infty}{B_{n,m}\cos\; v_{n}x\;\cos\;\mu_{m}y}}} & {A.\lbrack 15\rbrack} \\{{G \cdot y} = {\sum\limits_{n,{m = 1}}^{\infty}{D_{n,m}\cos\; p_{n}x\;\sin\; q_{m}y}}} & {A.\lbrack 16\rbrack}\end{matrix}$

The coefficients B_(n,m), and D_(n,m) are found to be

$\begin{matrix}{{B_{n,m} = {\frac{16\; B_{0}}{ab}\frac{\left( {- 1} \right)^{m + n}}{\mu_{m}v_{n}}}}{D_{n,m} = \frac{8{G\left( {- 1} \right)}^{m + n}}{p_{n}q_{m}a}}} & {A.\lbrack 17\rbrack}\end{matrix}$

The substitution of A.[12, 13, 15, 16] into A.[11] yields A_(n,m), andC_(n,m):

$\begin{matrix}{{A_{n,m} = {\frac{j\;{\omega\sigma}\; d}{\left( {v_{n}^{2} + \mu_{m}^{2}} \right)}B_{n,m}}}{C_{n,m} = \frac{{- j}\;\omega\; d\;\sigma\; D_{n,m}}{p_{n}^{2} + q_{m}^{2}}}} & {A.\lbrack 18\rbrack}\end{matrix}$

The total time-average eddy current power for the strip under thislinear gradient field can be calculated as:

$\begin{matrix}{\left\langle P \right\rangle = {\frac{d}{2\sigma}{\int_{{- b}/2}^{b/2}{\int_{{- a}/2}^{a/2}{\left( {{J_{x} \cdot J_{x}^{*}} + {J_{y} \cdot J_{y}^{*}}} \right)d\; x\; d\; y}}}}} & {A.\lbrack 19\rbrack}\end{matrix}$

Calculating the current density for both x and y components using A.[5]and A.[12, 13, 18], substituting into A.[19], and integrating over thewhole strip, reveals the total average power loss as:

$\begin{matrix}{\left\langle P \right\rangle = {\sum\limits_{n,{m = 1}}^{\infty}\left\lbrack {\frac{32\; B_{0}^{2}d\;{\sigma\omega}^{2}}{{abv}_{n}^{2}{\mu_{m}^{2}\left( {v_{n}^{2} + \mu_{m}^{2}} \right)}} + \frac{8G^{2}b\; d\;{\sigma\omega}^{2}}{{ap}_{n}^{2}{q_{m}^{2}\left( {p_{n}^{2} + q_{m}^{2}} \right)}}} \right\rbrack}} & {A.\lbrack 20\rbrack}\end{matrix}$

In A.[20], the first term provides corrections to equation [1], the eddycurrent power loss due to the homogeneous part in the field profile, andthe second term provides the power loss due to the y-gradient part infield profile. For example, if a slit is made in the x direction alongthe line y=y₀, which separates the strip into two narrower ones with newwidths, (y₀+b/2) and (b/2−y₀), respectively, then the magnetic fieldsaveraged over the areas of these two strips are:

$\begin{matrix}{{B_{0}^{(1)} = {\frac{1}{2}\left( {B_{0} + {G \cdot \left( {- \frac{b}{2}} \right)} + B_{0} + {G \cdot y_{0}}} \right)}}{B_{0}^{(2)} = {\frac{1}{2}\left( {B_{0} + {G \cdot \left( \frac{b}{2} \right)} + B_{0} + {G \cdot y_{0}}} \right)}}} & {A.\lbrack 21\rbrack}\end{matrix}$

Applying A.[20] to these two strips reveals the average powers for themto be:

$\begin{matrix}{\left\langle P_{1} \right\rangle = {\sum\limits_{n,{m = 1}}^{\infty}\left\lbrack {\frac{32\left( B_{0}^{(1)} \right)^{2}d\;{\sigma\omega}^{2}}{{a\left( {y_{0} + \frac{b}{2}} \right)}\left( {v_{n}^{(1)}\mu_{m}^{(1)}} \right)^{2}\left( {\left( v_{n}^{(1)} \right)^{2} + \left( \mu_{m}^{(1)} \right)^{2}} \right)} + \frac{8{G^{2}\left( {y_{0} + \frac{b}{2}} \right)}d\;{\sigma\omega}^{2}}{{a\left( {p_{n}^{(1)}q_{m}^{(1)}} \right)}^{2}\left( {\left( p_{n}^{(1)} \right)^{2} + \left( q_{m}^{(1)} \right)^{2}} \right)}} \right\rbrack}} & {A.\lbrack 22\rbrack} \\{\left\langle P_{2} \right\rangle = {\sum\limits_{n,{m = 1}}^{\infty}\left\lbrack {\frac{32\left( B_{0}^{(2)} \right)^{2}d\;{\sigma\omega}^{2}}{{a\left( {\frac{b}{2} - y_{0}} \right)}\left( {v_{n}^{(2)}\mu_{m}^{(2)}} \right)^{2}\left( {\left( v_{n}^{(2)} \right)^{2} + \left( \mu_{m}^{(2)} \right)^{2}} \right)} + \frac{8{G^{2}\left( {\frac{b}{2} - y_{0}} \right)}d\;{\sigma\omega}^{2}}{{a\left( {p_{n}^{(2)}q_{m}^{(2)}} \right)}^{2}\left( {\left( p_{n}^{(2)} \right)^{2} + \left( q_{m}^{(2)} \right)^{2}} \right)}} \right\rbrack}} & {A,\lbrack 23\rbrack}\end{matrix}$

The power ratio plots for different gradient strengths are generated byusing A.[20, 22, 23] to locate optimal cut positions.

Example apparatus and methods may employ an analysis based on A.[1]-[23]to place slots.

The following includes definitions of selected terms employed herein.The definitions include various examples and/or forms of components thatfall within the scope of a term and that may be used for implementation.The examples are not intended to be limiting. Both singular and pluralforms of terms may be within the definitions.

References to “one embodiment”, “an embodiment”, “one example”, and “anexample” indicate that the embodiment(s) or example(s) so described mayinclude a particular feature, structure, characteristic, property,element, or limitation, but that not every embodiment or examplenecessarily includes that particular feature, structure, characteristic,property, element or limitation. Furthermore, repeated use of the phrase“in one embodiment” does not necessarily refer to the same embodiment,though it may.

ASIC: application specific integrated circuit.

CD: compact disk.

CD-R: CD recordable.

CD-RW: CD rewriteable.

DVD: digital versatile disk and/or digital video disk.

LAN: local area network.

PCI: peripheral component interconnect.

PCIE: PCI express.

RAM: random access memory.

DRAM: dynamic RAM.

SRAM: synchronous RAM.

ROM: read only memory.

PROM: programmable ROM.

USB: universal serial bus.

WAN: wide area network.

“Computer component” as used herein, refers to a computer-related entity(e.g., hardware, firmware, software in execution, combinations thereof).Computer components may include, for example, a process running on aprocessor, a processor, an object, an executable, a thread of execution,and a computer. A computer component(s) may reside within a processand/or thread. A computer component may be localized on one computerand/or may be distributed between multiple computers.

“Computer-readable medium” as used herein, refers to a non-transitorymedium that stores signals, instructions and/or data. Acomputer-readable medium may take forms, including, but not limited to,non-volatile media, and volatile media. Non-volatile media may include,for example, optical disks, magnetic disks, and other disks. Volatilemedia may include, for example, semiconductor memories, dynamic memory,and other memories. Common forms of a computer-readable medium mayinclude, but are not limited to, a floppy disk, a flexible disk, a harddisk, a magnetic tape, other magnetic medium, an ASIC, a CD, otheroptical medium, a RAM, a ROM, a memory chip or card, a memory stick, andother media from which a computer, a processor or other electronicdevice can read.

“Logic” as used herein, includes but is not limited to hardware,firmware, software in execution on a machine, and/or combinations ofeach to perform a function(s) or an action(s), and/or to cause afunction or action from another logic, method, and/or system. Logic mayinclude a software-controlled microprocessor, a discrete logic (e.g.,ASIC), an analog circuit, a digital circuit, a programmed logic device,a memory device containing instructions, and other hardware. Logic mayinclude one or more gates, combinations of gates, or other circuitcomponents. Where multiple logical logics are described, it may bepossible to incorporate the multiple logical logics into one physicallogic. Similarly, where a single logical logic is described, it may bepossible to distribute that single logical logic between multiplephysical logics.

An “operable connection” or a connection by which entities are “operablyconnected”, is one in which signals, physical communications, and/orlogical communications may be sent and/or received. An operableconnection may include a physical interface, an electrical interface,and/or a data interface. An operable connection may include differingcombinations of interfaces and/or connections sufficient to allowoperable control. For example, two entities can be operably connected tocommunicate signals to each other directly or through one or moreintermediate entities (e.g., processor, operating system, logic,software). Logical and/or physical communication channels can be used tocreate an operable connection.

“Software” as used herein, includes but is not limited to, one or moreexecutable instructions that cause a computer, processor, or otherelectronic device to perform functions, actions and/or behave in adesired manner. “Software” does not refer to stored instructions beingclaimed as stored instructions per se (e.g., a program listing). Theinstructions may be embodied in various forms including routines,algorithms, modules, methods, threads, and/or programs includingseparate applications or code from dynamically linked libraries.

“User” as used herein, includes but is not limited to one or morepersons, software, logics, computers or other devices, or combinationsof these.

Some portions of the detailed descriptions that follow are presented interms of algorithms and symbolic representations of operations on databits within a memory. These algorithmic descriptions and representationsare used by those skilled in the art to convey the substance of theirwork to others. An algorithm, here and generally, is conceived to be asequence of operations that produce a result. The operations may includephysical manipulations of physical quantities. Usually, though notnecessarily, the physical quantities take the form of electrical ormagnetic signals capable of being stored, transferred, combined,compared, or otherwise manipulated in a logic. The physicalmanipulations create a concrete, tangible, useful, real-world result.

It has proven convenient at times, principally for reasons of commonusage, to refer to these signals as bits, values, elements, symbols,characters, terms, or numbers. It should be borne in mind, however, thatthese and similar terms are to be associated with the appropriatephysical quantities and are merely convenient labels applied to thesequantities. Unless specifically stated otherwise, it is to beappreciated that throughout the description, terms including processing,computing, determining, and analyzing, refer to actions and processes ofa computer system, logic, processor, or similar electronic device thatmanipulates and transforms data represented as physical (electronic)quantities.

Example methods may be better appreciated with reference to flowdiagrams. For purposes of simplicity of explanation, the illustratedmethodologies are shown and described as a series of blocks. However, itis to be appreciated that the methodologies are not limited by the orderof the blocks, as some blocks can occur in different orders and/orconcurrently with other blocks from that shown and described. Moreover,less than all the illustrated blocks may be required to implement anexample methodology. Blocks may be combined or separated into multiplecomponents. Furthermore, additional and/or alternative methodologies canemploy additional, not illustrated blocks.

FIG. 16 illustrates a method 1600 for designing a magnetic resonanceimaging (MRI) radio frequency (RF) shield. Method 1600 includes, at1610, identifying a desired degree of RF shielding to be achieved by theRF shield. Identifying the desired degree of RF shielding may include,for example, receiving a design parameter from a process, logic, oruser, calculating a degree of shielding needed for a procedure (e.g.,imaging procedure, image guided surgical procedure), or other actions.Recall that an ideal RF shield would be transparent to a gradient fieldproduced by a gradient coil in the MRI apparatus and would be opaque toan RF field produced by an RF transmission coil in the MRI apparatus.However, an ideal shield may not be required. Recall also that bothgradient fields and RF fields can induce eddy currents in an RF shield.The eddy currents can cause heating in the RF shield.

Thus, method 1600 includes, at 1620, identifying a desired heatingattribute for the RF shield. Example heating attributes include, forexample, a rate of change for temperature on the RF shield, a maximumtemperature on the RF shield, a temperature distribution on the RFshield, and other attributes. Different heating attributes may beassociated with different procedures. For example, a first higher rateof temperature change may be tolerable in a first type of MR guidedprocedure while a second lower rate of temperature change may berequired for a second type of MR guided procedure. Identifying thedesired heating attribute may include receiving a design parameter froma user, process, or apparatus. Identifying the desired heating attributemay also include analyzing strengths and durations of fields expectedduring procedure.

Heating in the RF shield depends on eddy currents induced in the RFshield and the eddy currents depend on the fields. Therefore method 1600includes, at 1630, identifying a gradient field to which the RF shieldwill be exposed. The gradient field will be produced by a gradient coilin the MRI apparatus. Method 1600 also includes, at 1640, identifying anRF field to which the RF shield will be exposed. The RF field will beproduced by an RF transmission coil in the MRI apparatus. Identifyingthe gradient field and the RF field may include receiving a designparameter from a user, process, or apparatus. Identifying the gradientfield and the RF field may also include predicting the strength andduration of fields expected during an MR procedure.

Method 1600 may also include, at 1650, determining whether a hot regionexists on the RF shield. A hot region may be identified as a region ofmaximal eddy current ohmic power. A hot region may also be identified asa region where a determined heating attribute does not satisfy thedesired heating attribute. The heating attribute can be determined indifferent ways. In one example, identifying the hot region involvesanalyzing gradient induced eddy current distribution on the RF shield.Analyzing gradient induced eddy current distribution on the RF shieldmay include identifying a region of maximal eddy current ohmic power onthe RF shield. In some examples, identifying the hot region may includeconsidering only gradient induced eddy current distribution due to an Xgradient coil and a Y gradient coil in the MRI apparatus.

If the determination at 1650 is yes, that a hot region exists, thenmethod 1600 proceeds, at 1660, to identify one or more axial cuts to bemade in the RF shield to reduce gradient eddy current heating producedin the RF shield by the gradient field. Method 1600 also includes, at1660, subsequently identifying one or more azimuthal cuts to be made inthe RF shield to further reduce gradient eddy current heating producedin the RF shield by the gradient field. In one embodiment the azimuthalcuts are identified after the axial cuts are produced.

The actions performed at 1660 identify axial cuts and azimuthal cutsthat will cause the RF shield to exhibit the desired heating attributewhile maintaining the desired degree of RF shielding. In one embodiment,the actions performed at 1660 determine the minimal number of axial cutsand azimuthal cuts that achieve the desired heating attribute whilemaintaining the desired RF shielding performance. In one embodiment, theazimuthal cuts are designed with azimuthal symmetry. In one embodiment,the azimuthal cuts are offset to account for rotating fields produced byquadrature operation of the MRI apparatus.

In one embodiment, method 1600 may also include controlling an automatedRF shield fabricator to cut the one or more axial cuts and the one ormore azimuthal cuts in the RF shield.

FIG. 17 illustrates additional detail for action 1660. The additionaldetail may include, at 1662, identifying a first region on the RF shieldto place axial cuts that will reduce a gradient induced eddy current inthe RF shield. The additional detail may also include, at 1664,designing the one or more axial cuts to make in the first region.Designing the axial cuts may involve determining the number, size,shape, and position of the axial cuts.

In one example, identifying the first region at 1662 involves analyzingRF eddy current patterns that would be induced in the RF shield by theRF field. In this example, designing the axial cuts at 1664 includesestablishing a position, length, and width for an axial cut that willreduce ohmic heating yet not impede an RF eddy current induced in the RFshield.

In another example, identifying the first region at 1662 involvesidentifying an RF current Z component dominant region in the RF shield.In this example, designing the axial cuts at 1664 includes restrictingthe axial cuts to be in the RF current Z component dominant region.

In another example, identifying the first region at 1662 involvesidentifying a domain [−Zc, +Zc] where the axial component RF inducedcurrent density is dominant. In this example, designing the axial cutsat 1664 includes establishing a position, length, and width for an axialcut based, at least in part, on the domain [−Zc, +Zc]. In oneembodiment, the [−Zc, +Zc] domain is identified by:∫₀ ^(π) |J _(z)(ϕ,z)|dϕ>∫ ₀ ^(π) |J _(ϕ)(ϕ,z)|dϕ for z∈[−Z _(c) ,+Z_(c)].

In yet another embodiment, identifying the first region at 1662 involvesmeasuring temperature on the RF shield while the RF shield is exposed tothe gradient field and the RF field.

The additional detail may also include, at 1666, identifying a secondregion on the RF shield to place azimuthal cuts that will reduce agradient induced eddy current in the RF shield. The location of thesecond region depends, at least in part, on attributes of the firstregion. The attributes can include, for example, the size of the firstregion, the shape of the first region, the position of the first region,and the size, shape, orientation, and number of axial cuts in the firstregion. The additional detail may also include, at 1668, designing theazimuthal cuts to make in the second region.

In one embodiment, identifying the second region at 1666 involvesidentifying a cold band where there is minimal eddy current ohmic poweron the RF shield. In this example, designing the azimuthal cut at 1668may involve placing the azimuthal cut in or near the cold band. Inanother embodiment, identifying the second region at 1666 may be based,at least in part, on simulating a power ratio for one or more potentialazimuthal slit positions. In this example, designing the azimuthal cutat 1668 may involve placing an azimuthal cut based on a minimaidentified in a power curve produced during the simulation. In oneembodiment, method 1600 may iterate through actions 1666 and 1668 untila termination condition is satisfied.

In one embodiment, identifying the second region at 1666 involvesmeasuring temperature on the RF shield while the RF shield is exposed tothe gradient field and the RF field. In this embodiment, designing theazimuthal cut may involve placing the cut in a region with a minimaltemperature.

While FIGS. 16 and 17 illustrates various actions occurring in serial,it is to be appreciated that various actions illustrated in FIGS. 16 and17 could occur substantially in parallel. By way of illustration, afirst process could identify fields, a second process could identifydesign requirements (e.g., shielding, heating attribute), a thirdprocess could identify regions and a fourth process could design cuts.While four processes are described, it is to be appreciated that agreater and/or lesser number of processes could be employed and thatlightweight processes, regular processes, threads, and other approachescould be employed. Additionally, while FIGS. 16 and 17 show a singleiteration through method 1600, various actions could be iterated over.

In one example, a method may be implemented as computer executableinstructions. Thus, in one example, a computer-readable medium may storecomputer executable instructions that if executed by a machine (e.g.,processor) cause the machine to perform method 1600. While executableinstructions associated with method 1600 are described as being storedon a computer-readable medium, it is to be appreciated that executableinstructions associated with other example methods described herein mayalso be stored on a computer-readable medium.

FIG. 18 illustrates an example computing device in which example systemsand methods described herein, and equivalents, may operate. The examplecomputing device may be a computer 1800 that includes a processor 1802,a memory 1804, and input/output ports 1810 operably connected by a bus1808. In one example, the computer 1800 may include a pattern logic 1830configured to identify the pattern of axial and azimuthal cuts to bemade in an RF shield. In different examples, the logic 1830 may beimplemented in hardware, software, firmware, and/or combinationsthereof. While the logic 1830 is illustrated as a hardware componentattached to the bus 1808, it is to be appreciated that in one example,the logic 1830 could be implemented in the processor 1802.

Logic 1830 may provide means (e.g., hardware, software, firmware) foridentifying a set of axial cuts to be made in an RF shield. The set ofaxial cuts may be determined, at least in part, on an effect an axialcut would have on reducing gradient field induced eddy currents in theRF shield. Logic 1830 may also provide means (e.g., hardware, software,firmware) for identifying a set of azimuthal cuts to be made in the RFshield. The set of azimuthal cuts are determined, at least in part, onan effect an azimuthal cut would have on reducing gradient field inducededdy currents in the RF shield. Logic 1830 may also provide means forcontrolling an RF shield fabricator to configure the RF shield with theset of axial cuts and the set of azimuthal cuts. The means associatedwith logic 1830 may be implemented, for example, as an ASIC programmedto design and implement the pattern. The means may also be implementedas computer executable instructions that are presented to computer 1800as data 1816 that are temporarily stored in memory 1804 and thenexecuted by processor 1802.

Generally describing an example configuration of the computer 1800, theprocessor 1802 may be a variety of various processors including dualmicroprocessor and other multi-processor architectures. A memory 1804may include volatile memory and/or non-volatile memory. Non-volatilememory may include, for example, ROM, PROM, and other memory. Volatilememory may include, for example, RAM, SRAM, DRAM, and other memory.

A disk 1806 may be operably connected to the computer 1800 via, forexample, an input/output interface (e.g., card, device) 1818 and aninput/output port 1810. The disk 1806 may be, for example, a magneticdisk drive, a solid state disk drive, a floppy disk drive, a tape drive,a Zip drive, a flash memory card, a memory stick, and other storage.Furthermore, the disk 1806 may be a CD-ROM drive, a CD-R drive, a CD-RWdrive, a DVD ROM drive, a Blu-Ray drive, an HD-DVD drive, or otherdrive. The memory 1804 can store a process 1814 and/or a data 1816, forexample. The disk 1806 and/or the memory 1804 can store an operatingsystem that controls and allocates resources of the computer 1800.

The bus 1808 may be a single internal bus interconnect architectureand/or other bus or mesh architectures. While a single bus isillustrated, it is to be appreciated that the computer 1800 maycommunicate with various devices, logics, and peripherals using otherbusses (e.g., PCIE, 1394, USB, Ethernet). The bus 1808 can be typesincluding, for example, a memory bus, a memory controller, a peripheralbus, an external bus, a crossbar switch, and/or a local bus.

The computer 1800 may interact with input/output devices via the i/ointerfaces 1818 and the input/output ports 1810. Input/output devicesmay be, for example, a keyboard, a microphone, a pointing and selectiondevice, cameras, video cards, displays, the disk 1806, the networkdevices 1820, a metal fabrication device, and other devices. Theinput/output ports 1810 may include, for example, serial ports, parallelports, and USB ports.

The computer 1800 can operate in a network environment and thus may beconnected to the network devices 1820 via the i/o interfaces 1818,and/or the i/o ports 1810. Through the network devices 1820, thecomputer 1800 may interact with a network. Through the network, thecomputer 1800 may be logically connected to remote computers. Networkswith which the computer 1800 may interact include, but are not limitedto, a LAN, a WAN, and other networks. A metal fabrication device may beoperably connected to computer 1800 through the network devices 1820.

FIG. 19 illustrates an apparatus 1900. Apparatus 1900 includes aprocessor 1910, a memory 1920, a set 1930 of logics, and an interface1940 to connect the processor 1910, the memory 1920, and the set 1930 oflogics. In one embodiment the set 1930 of logics is configured to designa pattern of axial cuts and azimuthal cuts to be made in an RF shieldfor use with an MRI apparatus. In one embodiment, apparatus 1900 may bea special purpose computer that is created as a result of programming ageneral purpose computer. In another embodiment, apparatus 1900 mayinclude special purpose circuits that are added to a general purposecomputer to produce a special purpose computer.

In one embodiment, the set 1930 of logics includes a first logic 1932, asecond logic 1934, a third logic 1936 and a fourth logic 1938. In oneembodiment, the first logic 1932 is configured to identify a first(e.g., central) region of the RF shield in which axial cuts are to bemade to reduce ohmic heating of the RF shield due to gradient inducededdy currents.

In one embodiment, the second logic 1934 is configured to establish alimit for the length of the axial cuts based on a high frequencyelectromagnetic analysis of RF induced eddy current patterns in the RFshield.

In one embodiment, the third logic 1936 is configured to establish asecond (e.g., end ring) region in the RF shield in which azimuthal cutsare to be made to reduce ohmic heating of the RF shield due to gradientinduced eddy currents. The third logic 1936 is configured to determinethe size and location of the end ring region based, at least in part, onthe location and size of the central region and on the axial cuts in thecentral region.

In one embodiment, the fourth logic 1938 is configured to determine anumber of 360 degree azimuthal cuts to be made through the end ringregion. The fourth logic 1938 may be configured to determine the numberof cuts based on a degree of ohmic power reduction produced by the axialcuts and azimuthal cuts as determined by a low frequency electromagneticgradient current analysis.

FIG. 20 illustrates an example RF shield 2000. Attributes of shield 2000may be designed by example methods and apparatus described herein. Inone embodiment, RF shield 2000 may be a printed circuit board radiofrequency (RF) shield for use with a hybrid magnetic resonance imaging(MRI) apparatus. The RF shield 2000 may include a dielectric materiallayer 2020, a first copper sheet 2010 attached to a first side of thedielectric material 2020 and a second copper sheet 2030 attached to asecond, different side of the dielectric material 2020.

In one embodiment, the first copper sheet 2010 includes a first set ofaxial cuts 2014 that are sized and positioned to reduce ohmic heatingdue to eddy currents induced in the RF shield 2000 by a split X-gradientcoil in the MRI apparatus without disrupting eddy currents induced inthe RF shield by an RF transmission coil in the MRI apparatus. The firstcopper sheet 2010 may also include a first set of azimuthal cuts 2012and 2016. The azimuthal cuts 2012 and 2016 may be sized and positionedto reduce ohmic heating due to eddy currents induced in the RF shield bythe split X-gradient coil. While two azimuthal cuts 2012 and 2016 areillustrated, a greater and/or lesser number of azimuthal cuts may beemployed.

In one embodiment, the second copper sheet 2030 also includes a secondset of axial cuts 2034 that are sized and positioned to reduce ohmicheating due to eddy currents induced in the RF shield 2000 by a splitY-gradient coil in the MRI apparatus. The second set of axial cuts 2034are sized and positioned to not disrupt eddy currents induced in the RFshield by the RF transmission coil. In this embodiment, the secondcopper sheet 2030 also includes a second set of azimuthal cuts 2032 and2036 that are sized and positioned to reduce ohmic heating due to eddycurrents induced in the RF shield by the split Y-gradient coil.

In one embodiment of RF shield 2000, at least one of, a length, a width,and a position of a member of the first set of axial cuts, a member ofthe second set of axial cuts, a member of the first set of azimuthalcuts, and a member of the second set of azimuthal cuts are determined,at least in part, by eddy current pattern distributions on the firstcopper sheet and the second copper sheet.

In one embodiment of printed circuit board RF shield 2000, the first setof axial cuts 2014 and the first set of azimuthal cuts 2012 and 2016 arepositioned with respect to the second set of axial cuts 2034 and thesecond set of azimuthal cuts 2032 and 2036 to account for rotatingfields produced by quadrature operation of a hybrid MRI system.

While example apparatus, methods, and other embodiments have beenillustrated by describing examples, and while the examples have beendescribed in considerable detail, it is not the intention of theapplicants to restrict or in any way limit the scope of the appendedclaims to such detail. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing the apparatus, methods, and other embodiments describedherein. Therefore, the invention is not limited to the specific details,the representative apparatus, and illustrative examples shown anddescribed. Thus, this application is intended to embrace alterations,modifications, and variations that fall within the scope of the appendedclaims.

To the extent that the term “includes” or “including” is employed in thedetailed description or the claims, it is intended to be inclusive in amanner similar to the term “comprising” as that term is interpreted whenemployed as a transitional word in a claim.

To the extent that the term “or” is employed in the detailed descriptionor claims (e.g., A or B) it is intended to mean “A or B or both”. Whenthe applicants intend to indicate “only A or B but not both” then theterm “only A or B but not both” will be employed. Thus, use of the term“or” herein is the inclusive, and not the exclusive use. See, Bryan A.Garner, A Dictionary of Modern Legal Usage 624 (2d. Ed. 1995).

To the extent that the phrase “one or more of, A, B, and C” is employedherein, (e.g., a data store configured to store one or more of, A, B,and C) it is intended to convey the set of possibilities A, B, C, AB,AC, BC, ABC, AAA, AAB, AABB, AABBC, AABBCC, etc. (e.g., the data storemay store only A, only B, only C, A&B, A&C, B&C, A&B&C, A&A&A, A&A&B,A&A&B&B, A&A&B&B&C, A&A&B&B&C&C, etc.). It is not intended to requireone of A, one of B, and one of C. When the applicants intend to indicate“at least one of A, at least one of B, and at least one of C”, then thephrasing “at least one of A, at least one of B, and at least one of C”will be employed.

Throughout this specification and the claims that follow, unless thecontext requires otherwise, the words ‘comprise’ and ‘include’ andvariations such as ‘comprising’ and ‘including’ will be understood to beterms of inclusion and not exclusion. For example, when such terms areused to refer to a stated integer or group of integers, such terms donot imply the exclusion of any other integer or group of integers.

What is claimed is:
 1. A radio frequency (RF) shield for use with asplit magnetic resonance imaging (MRI) apparatus, comprising: adielectric material layer; a first sheet attached to a first side of thedielectric material layer; and a second sheet attached to a second,different side of the dielectric material layer, where the first sheetincludes a first set of axial cuts sized and positioned to reduce ohmicheating due to eddy currents induced in the RF shield by a splitX-gradient coil in the split MRI apparatus in the split MRI apparatus,where the first sheet includes a first set of azimuthal cuts sized andpositioned to reduce ohmic heating due to eddy currents induced in theRF shield by the split X-gradient coil, where the second sheet includesa second set of axial cuts sized and positioned to reduce ohmic heatingdue to eddy currents induced in the RF shield by a split Y-gradient coilin the split MRI apparatus, where the second sheet includes a second setof azimuthal cuts sized and positioned to reduce ohmic heating due toeddy currents induced in the RF shield by the split Y-gradient coil. 2.The RF shield of claim 1, where the first set of axial cuts and thefirst set of azimuthal cuts are positioned with respect to the secondset of axial cuts and the second set of azimuthal cuts to account forrotating fields produced by quadrature operation of the split MRIsystem.
 3. The RF shield of claim 1, where at least one of, a length, awidth, and a position of a member of the first set of axial cuts, amember of the second set of axial cuts, a member of the first set ofazimuthal cuts, and a member of the second set of azimuthal cuts aredetermined, at least in part, by eddy current pattern distributions onthe first sheet and the second sheet.
 4. A printed circuit board radiofrequency (RF) shield for use with a split magnetic resonance imaging(MRI) apparatus having a split x-gradient coil, a split y-gradient coil,and an RF transmission coil, comprising: a dielectric material layer; afirst metallic sheet attached to or in contact with a first side of thedielectric material layer; and a second metallic sheet attached to or incontact with a second, different side of the dielectric material layer,where the first metallic sheet includes a first set of axial cutspositioned in a region where an x-gradient coil eddy current induced inthe printed circuit board RF shield by the split x-gradient coil exceedsan x-gradient coil threshold density level, and where an RF transmissioncoil eddy current induced in the printed circuit board RF shield by theRF transmission coil is less than a first RF transmission coil eddycurrent density level; where the first metallic sheet includes a firstset of azimuthal cuts positioned in a region where the RF transmissioncoil eddy currents induced in the printed circuit board RF shield by theRF transmission coil are greater than a second RF transmission coil eddycurrent density level, where the second metallic sheet includes a secondset of axial cuts positioned in a region where a y-gradient coil eddycurrent induced in the printed circuit board RF shield by the splity-gradient coil exceeds a y-gradient coil threshold density level, andwhere the RF transmission coil eddy current induced in the printedcircuit board RF shield by the RF transmission coil are less than athird RF transmission coil eddy current density level, where the secondmetallic sheet includes a second set of azimuthal cuts positioned in aregion where the RF transmission coil eddy current induced in theprinted circuit board RF shield by the RF transmission coil is greaterthan a fourth RF transmission coil eddy current density level, where thefirst set of axial cuts and the first set of azimuthal cuts reduce ohmicheating due to the x-gradient coil eddy current without reducing RFshielding, and where the second set of axial cuts and the second set ofazimuthal cuts reduce ohmic heating due to the y-gradient coil eddycurrent without reducing RF shielding.
 5. The printed circuit board RFshield of claim 4, where the x-gradient coil eddy current has a densitydescribed by:${{J_{\phi}\left( {\phi,z} \right)} = {\frac{\partial}{\partial z}{S\left( {\phi,z} \right)}}};{{J_{z}\left( {\phi,z} \right)} = {{- \frac{1}{R_{s}}}\frac{\partial}{\partial\phi}{S\left( {\phi,z} \right)}}}$where J is the eddy current density (A/m²).
 6. The printed circuit boardRF shield of claim 4, where the y-gradient coil eddy current has adensity described by:${{J_{\phi}\left( {\phi,z} \right)} = {\frac{\partial}{\partial z}{S\left( {\phi,z} \right)}}};{{J_{z}\left( {\phi,z} \right)} = {{- \frac{1}{R_{s}}}\frac{\partial}{\partial\phi}{S\left( {\phi,z} \right)}}}$where J is the eddy current density (A/m²).
 7. The printed circuit boardRF shield of claim 4, where the RF transmission coil eddy current has adensity described by:${{J_{\phi}\left( {\phi,z} \right)} = {\frac{\partial}{\partial z}{S\left( {\phi,z} \right)}}};{{J_{z}\left( {\phi,z} \right)} = {{- \frac{1}{R_{s}}}\frac{\partial}{\partial\phi}{S\left( {\phi,z} \right)}}}$where J is the eddy current density (A/m²).
 8. The printed circuit boardRF shield of claim 4, where the printed circuit board RF shield istransparent to a gradient field produced by the split x-gradient coiland a gradient field produced by the split y-gradient coil, and wherethe printed circuit board RF shield is opaque to an RF field produced bythe RF transmission coil.
 9. The printed circuit board RF shield ofclaim 4, where one or more of the position, length, and width of amember of the first set of axial cuts is based, at least in part, on afirst region domain [−Zc, +Zc].
 10. The printed circuit board RF shieldof claim 9, where the first region domain [−Zc, +Zc] is described by:∫₀^(π)J_(z)(ϕ, z)d ϕ > ∫₀^(π)J_(ϕ)(ϕ, z)d ϕ  for  z ∈ [−Zc, +Zc].11. The printed circuit board RF shield of claim 4, where one or moremembers of the first set of azimuthal cuts or the second set ofazimuthal cuts are located at positions corresponding to, at least inpart, the region of minimal eddy current ohmic power on the printedcircuit board RF shield.
 12. The printed circuit board RF shield ofclaim 4, where one or more members of the first set of azimuthal cutsare located in a region corresponding to the minimal value of a powercurve.
 13. The printed circuit board RF shield of claim 4, where one ormore members of the first set of azimuthal cuts or the second set ofazimuthal cuts display azimuthal symmetry.
 14. The printed circuit boardRF shield of claim 4, where one or more members of the first set ofazimuthal cuts or the second set of azimuthal cuts are offset to accountfor a rotating field produced by quadrature operation of the split MRIapparatus.
 15. The printed circuit board RF shield of claim 4, where theregion where the x-gradient coil eddy current exceeds an x-gradient coilthreshold density level corresponds to a fingerprint eye of a splitgradient coil employed in a split MRI system.
 16. The printed circuitboard RF shield of claim 4, where the region where the RF transmissioncoil eddy current is less than a first RF transmission coil eddy currentdensity level corresponds to a fingerprint eye of a split gradient coilemployed in a split MRI system.
 17. The printed circuit board RF shieldof claim 4, where the region where the y-gradient coil eddy currentexceeds a y-gradient coil threshold density level corresponds to afingerprint eye of a split gradient coil employed in a split MRI system.18. The printed circuit board RF shield of claim 4, where the regionwhere the RF transmission coil eddy current is less than a third RFtransmission coil eddy current density level corresponds to afingerprint eye of a split gradient coil employed in a split MRI system.19. The printed circuit board RF shield of claim 4, where one or moremembers of the first set of axial cuts is spanned by a capacitor. 20.The printed circuit board RF shield of claim 4, where one or moremembers of the first set of azimuthal cuts is spanned by a capacitor.21. The printed circuit board RF shield of claim 4, where one or moremembers of the second set of axial cuts is spanned by a capacitor. 22.The printed circuit board RF shield of claim 4, where one or moremembers of the second set of azimuthal cuts is spanned by a capacitor.23. A radio frequency (RF) shield for use with a split magneticresonance imaging (MRI) apparatus, comprising: a dielectric materiallayer; a first sheet attached to a first side of the dielectric materiallayer; and a second sheet attached to a second, different side of thedielectric material layer, where the first sheet includes a first set ofaxial cuts and a first set of azimuthal cuts, and where the second sheetincludes a second set of axial cuts and a second set of azimuthal cuts.